In Young’s two slit experiment, the first dark fringe above the central bright fringe occurs at an angle of 0.44˚. What is the ratio of the slit separation, d, to the wavelength of the light, λ

d / λ = 26.7

Explanation:

In Young's double slit experiment, constructive interference is described by the expression

   d sin θ = m λ

In the case of destructive interference we must add half wavelength (λ/2)

   d siyn θ = (m + ½) λ

Let's clear

    d / λ = (m + ½) / sin θ

Let's calculate

   d / λ = (2+ ½) / sin 5.4

   d / λ = 5 / (2 sin 5.4)

   d / λ = 26.7